Solutions for Session 7, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6| A7| A8| A9| A10

 Problem A1 No, the data are not sorted by height; for example, the first three heights are 162 cm, 160 cm, and 162 cm. However, the data generally appear to be listed in increasing order. The wider we find a person's arm span to be, the greater we might expect that person's height to be, although clearly there is some variation to this rule. The fact that height generally appears in increasing order suggests a positive association between height and arm span.

Problem A2

 a. Answers will vary. b. Answers will vary, but generally the recorded information should sustain the observation that there is a positive association between height and arm span. c. Answers will vary.

 Problem A3 Yes, there appears to be a positive association. In general, the points in the graph move up and to the right. There are exceptions to this, but typically, an increase in arm span leads to an increase in height.

Problem A4

 a. Answers will vary. b. Twelve of the 24 people have above-average arm spans. c. Thirteen of the 24 people have above-average heights. d. Eleven people have above-average arm spans and heights. One person has an above-average arm span but a below-average height. Two people have below-average arm spans but above-average heights. Ten people have below-average arm spans and heights.

Problem A6

 a. No, this will not always happen, because we are considering the mean and not the median. The mean is not necessarily the median of the data; for example, when considering the heights for this group, we see that 13 people are above the mean and 11 are below it. b. Anyone whose point is to the right of this line has an above-average arm span. In contrast, anyone whose point is to the left of the line has a below-average arm span.

 Problem A7 Anyone whose point appears above this line has an above-average height. There are 13 such points.

Problem A9

 a. People in Quadrant I have above-average arm spans and heights. b. People in Quadrant II have below-average arm spans and above-average heights. c. People in Quadrant III have below-average arm spans and heights. d. People in Quadrant IV have above-average arm spans and below-average heights.

Problem A10

 a. Yes, most people who have above-average arm spans also have above-average heights. By counting the points, we can see that 11 of the 12 people with above-average arm spans also have above-average heights. b. Yes, most people who have below-average arm spans also have below-average heights. By counting the points, we can see that 10 of the 12 people with below-average arm spans also have below-average heights.